Abstract
This paper describes a novel seismic optimal design method for the reinforced concrete frame. First, an optimal mathematical model with time-dependent constraints, i.e., inter-story drift constraints, is established for achieving minimum weight design. Second, the inequality constraint problem with time-dependent constraints is converted into a sequence of appropriately formed unconstrained problems using the integral interior point penalty function method. Third, an efficient algorithm of the first and second derivatives of the inter-story drift with respect to design variables is formulated based on Newmark-β method. Gradient and Hessian matrix of the integral interior penalty function are also computed. Fourth, Marquardt’s method is employed to solve a sequence of unconstrained problems. Finally, the minimum weight design of a three-story, two-bay planar frame is demonstrated using the new optimization method and the augmented Lagrange multiplier method. The comparative results show the seismic optimal design method presented in this paper is more efficient than the augmented Lagrange multiplier method in terms of computational time. The proposed new method is an effective and efficient approach for minimum weight design of the reinforced concrete frames subjected to earthquake excitation.
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Liu, Q., Zhang, J. & Yan, L. An optimal method for seismic drift design of concrete buildings using gradient and Hessian matrix calculations. Arch Appl Mech 80, 1225–1242 (2010). https://doi.org/10.1007/s00419-009-0368-0
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DOI: https://doi.org/10.1007/s00419-009-0368-0